There are calories in 1 order of Sonic Drive-In Mozzarella Sticks (6 pieces). You'd need to walk minutes to burn calories. Visit CalorieKing to see. Calories in Sonic Drive In Mozzarella Sticks 5. Find nutrition facts for Sonic Drive In Mozzarella Sticks 5 and over other foods in frogcitycheese.com's. Don't ignore your snack cravings, even when you are ordering a combo meal. That's right, our snacks are sides and our sides are snacks.